Astm f 1390 97

F 1390 – 97 Designation F 1390 – 97 Standard Test Method for Measuring Warp on Silicon Wafers by Automated Noncontact Scanning 1 This standard is issued under the fixed designation F 1390; the number[.]

Standard Test Method for

Measuring Warp on Silicon Wafers by Automated

This standard is issued under the fixed designation F 1390; the number immediately following the designation indicates the year of

original adoption or, in the case of revision, the year of last revision A number in parentheses indicates the year of last reapproval A

superscript epsilon (e) indicates an editorial change since the last revision or reapproval.

1 Scope

1.1 This test method covers a noncontacting, nondestructive

procedure to determine the warp of clean, dry semiconductor

wafers

1.2 The test method is applicable to wafers 50 mm or larger

in diameter, and 100 µm (0.004 in.) approximately and larger in

thickness, independent of thickness variation and surface

finish, and of gravitationally-induced wafer distortion

1.3 This test method is not intended to measure the flatness

of either exposed silicon surface Warp is a measure of the

distortion of the median surface of the wafer

1.4 This test method measures warp of a wafer corrected for

all mechanical forces applied during the test Therefore, the

procedure described gives the unconstrained value of warp

This test method includes a means of canceling

gravity-induced deflection which could otherwise alter the shape of the

wafer.2 The resulting parameter is described by Warp(2) in

Appendix X2 Shape Decision Tree in SEMI Specification M 1

(See Annex A1.)

N OTE 1—Test Method F 657 measures median surface warp using a

three-point back-surface reference plane The back-surface reference

results in thickness variation being included in the recorded warp value.

The use (in this test method) of a median surface reference plane

eliminates this effect The use (in this test method) of a least-squares fit

reference plane reduces the variability introduced in three-point plane

calculations by choice of reference point location The use (in this test

method) of special calibration or compensating techniques minimizes the

effects of gravity-induced distortion of the wafer.

1.5 The values stated in SI units are to be regarded

sepa-rately as the standard The values given in parentheses are for

information only

1.6 This standard does not purport to address all of the

safety concerns, if any, associated with its use It is the

responsibility of the user of this standard to establish

appro-priate safety and health practices and determine the

applica-bility of regulatory limitations prior to use.

2 Referenced Documents

2.1 ASTM Standards:

F 657 Test Method for Measuring Warp and Total Thickness Variation on Silicon Slices and Wafers by Noncontact Scanning3

F 1241 Terminology of Silicon Technology3

2.2 SEMI Standard:

M 1 Specifications for Polished Monocrystalline Silicon Wafers4

3 Terminology

3.1 Definitions:

3.1.1 mechanical signature— of an instrument, that

compo-nent of a measurement that is introduced by the instrument and that is systematic, repeatable, and quantifiable

3.1.2 median surface—of a semiconductor wafer, the locus

of points equidistant from the front and back surfaces

3.1.3 quality area—that portion of a wafer within the

specified parameter is determined

3.1.4 reference plane— of a semiconductor wafer, a plane

from which deviations are measured

3.1.5 reference plane deviation (RPD)—the distance from a

point on a reference plane to the corresponding point on a wafer surface A dome-shaped wafer is considered to have positive RPD at its center; a bowl-shaped wafer is considered

to have negative RPD at its center

3.1.6 thickness—of a semiconductor wafer, the distance

through the wafer between corresponding points on the front and back surfaces

3.1.7 wafer—of a semiconductor, the difference between

the maximum and minimum distances of the median surface of

a free, unclamped wafer from a reference plane

3.1.7.1 Discussion—Although warp may be caused by

un-equal stresses on the two exposed surfaces of the wafer, it cannot be determined from measurements on a single exposed surface The median surface may contain regions with upward

or downward curvature or both; under some conditions the median surface may be flat (see figures in Appendix X1) 3.2 Other definitions relative to silicon material technology can be found in Terminology F 1241

1

This test method is under the jurisdiction of ASTM Committee F-1 on

Electronicsand is the direct responsibility of Subcommittee F01.06 on Silicon

Materials and Process Control.

Current edition approved June 10, 1997 Published August 1997 Originally

published as F 1390–92 Last previous edition F 1390–92{1.

2 Poduje, N., “Eliminating Gravitational Effect in Wafer Shape Measurements,”

NIST/ASTM/SEMI/SEMATECH Technology Conference, Dallas, TX; Technology

for Advanced Materials/Process Characterization, February 1, 1990.

3

Annual Book of ASTM Standards, Vol 10.05.

4 Available from SEMI, 805 East Middlefield Road, Mt View, CA 94043.

1

AMERICAN SOCIETY FOR TESTING AND MATERIALS

100 Barr Harbor Dr., West Conshohocken, PA 19428 Reprinted from the Annual Book of ASTM Standards Copyright ASTM

4 Summary of Test Method

4.1 A calibration procedure is performed In addition to

setting the instrument’s scale factor and other constants, this

procedure determines the mechanical signature of the

instru-ment and the effect of gravity on the wafer

4.2 The wafer is supported by a small-area chuck and both

external surfaces are simultaneously scanned along a

pre-scribed pattern by both members of an opposed pair of probes

4.3 The paired displacement values are used to construct a

median surface

4.4 The median surface is mathematically corrected for

gravitational effects and for mechanical signature of the

instru-ment

4.5 A least-squares reference plane is constructed from the

corrected median surface

4.6 The reference plane deviation (RPD) is calculated at

each measured point

4.7 Warp is reported as the algebraic difference between the

most positive RPD and the most negative RPD

5 Significance and Use

5.1 Warp can significantly affect the yield of semiconductor

device processing

5.2 Knowledge of this characteristic can help the producer

and consumer determine if the dimensional characteristics of a

specimen wafer satisfy given geometrical requirements

5.3 Changes in wafer warp during processing can adversely

affect subsequent handling and processing steps These

changes can also provide an important process monitoring

function

5.4 The test method is suitable for measuring the warp of

wafers used in semiconductor device processing in the

as-sliced, lapped, etched, polished, epitaxial, or other layer

condition and for monitoring thermal and mechanical effects

on the warp of wafers during device processing

5.5 Until the results of a planned interlaboratory evaluation

of this test method are established, use of this test method for

commercial transactions is not recommended unless the parties

to the test establish the degree of correlation that can be

obtained

6 Interferences

6.1 Any relative motion along the probe measuring axis

between the probes and the wafer holding device during

scanning will produce error in the measurement data Vibration

of the test specimen relative to the probe-measuring axis will

introduce error Such errors are minimized by system signature

analysis and correction algorithms Internal system monitoring

may also be used to correct non-repetitive and repetitive

system mechanical translations, and failure to provide such

corrections may cause errors

6.2 If a measured wafer differs substantially in diameter,

thickness, fiducials or crystal orientation from that used for the

gravitational compensation procedure, the results may be

incorrect Approximate errors for differences in diameter and

thickness are shown in Appendix X2 If the crystal orientation

of the sample to be measured differs from the crystal

orienta-tion of the gravity-compensaorienta-tion wafer, then the measured

warp value may differ from the actual warp value by up to

15 % Error tables for fiducial variation have not been gener-ated

6.3 Different methods for implementing gravitational pensation may give different results Varying levels of com-pleteness of implementing a method may also give different results

N OTE 2—The recommended method for gravitational compensation is representative wafer inversion, 5 since it allows the use of a single wafer

to establish the compensation that is subsequently applied to sample wafers The sample wafer inversion method requires that every wafer be measured twice, once in a normal and once in an inverted position, which increases measurement time and subjects the sample to additional han-dling Theoretical modeling requires only a single measurement per sample, however it does not address machine signature issues, nor is a rigorous theory presently known to exist.

6.4 Mechanical variations in wafer holding devices between systems may introduce measurement differences See 7.1.1 6.5 Most equipment systems capable of this measurement have a definite range of wafer thickness combined with warp (dynamic range) that can be accommodated without readjust-ment If the sample moves outside this dynamic range during either calibration or measurement, results may be in error An overrange signal can be used to alert the operator and mea-surement data examiners to this event

6.6 The quantity of data points and their spacing may affect the measurement results See 7.1.2

7 Apparatus

7.1 Warp-Measuring Equipment, consisting of wafer

hold-ing device, multiple-axis transport mechanism, probe assembly with indicator, and system controller/computer, including data processor and suitable software The system must be equipped with an overrange signal Instrument data reporting resolution shall be 100 nm or smaller

7.1.1 Wafer-Holding Device, for example a chuck whose

face is perpendicular to the measurement axis, and on which the wafer is placed for the measurement scan The diameter of the wafer holding device shall be 22-mm (0.9-in.) diameter, 33-mm (1.3-in.) diameter, or other value as agreed upon between using parties

7.1.2 Multiple-Axis Transport Mechanism, which provides a

means for moving the wafer-holding device, or the probe assembly, perpendicularly to the measurement axis in a con-trolled fashion in several axes This motion must permit data gathering over a prescribed scan pattern the entire quality area Maximum data point spacing to be used shall be 4 mm, or other value as agreed upon between using parties

7.1.3 Probe Assembly With Paired Non-Contacting Displacement-Sensing Probes, Probe Supports, and Indicator Unit—The probes shall be capable of independent

measure-ment of the distance between the probed site on each surface of the sample wafer and the motion plane The probes shall be mounted above and below the wafer in a manner so that the probed site on one surface of the wafer is opposite the probed site on the other The common axis of these probes is the

5 The representative wafer method of gravitational correction is covered by a patent held by ADE Corporation, 77 Rowe Street, Newton, MA 02166 Alternate methods are described in 13.1.2.

2

measurement axis (see Fig 1 ) The probe separation D shall be

kept constant during calibration and measurement

Displacement resolution shall be 0.1 µm or better The probe

sensor size shall be 4 by 4 mm, or other value to be agreed

upon between using parties Systems employing either

representative wafer inversion of sample wafer inversion

methods for gravity compensation must provide precise

positioning in both measurement orientations so that

measurements are taken at identical locations for each

orientation of the sample

where:

D 5 the distance from probe b to probe a,

a 5 the distance from the top surface of the wafer to probe

a,

b 5 the distance from probe b to the bottom surface of the

water,

t 5 wafer thickness, (always a positive number) and

z 5 the distance between the wafer medium surface and

the point halfway between the upper and lower

probes

8 Materials

8.1 Set-up Masters, suitable to accomplish calibration and

standardization as recommended by the equipment

manufacturer

8.2 Reference Wafer, the warp value#20 µm with a data set

that is used to determine the level of agreement between the

system under test and the data set (see Annex A1)

8.3 Representative Wafer—If using the representative wafer

inversion method, a wafer identical in nominal diameter,

thickness, fiducials, composition and crystalline orientation to

those being measured is required for the calibration procedure

Its warp need not be known

9 Suitability of Test Equipment

9.1 The suitability of the test equipment shall be determined

with the use of a reference wafer and its associated data set in

accordance with the procedures of Annex A1, or by

performance of a statistically-based instrument repeatability study to ascertain whether the equipment is operating within the manufacturer’s stated specification for repeatability

N OTE 3—For further information on instrument repeatability studies contact Subcommittee F1.95.

9.2 Determination of degree of suitability is currently under investigation

10 Sampling

10.1 This test method is nondestructive and may be used on either 100 % of the wafers in a lot or on a sampling basis 10.1.1 If samples are to be taken, procedures for selecting the sample from each lot of wafers to be tested shall be agreed upon by the parties to the test, as shall the definition of what constitutes a lot

11 Calibration and Standardization

11.1 Calibrate in accordance with the manufacturer’s instructions

12 Procedure

12.1 Prepare the apparatus for measurement of wafers, including selection of diameter, peripheral fiducials, scan area, and data display/output functions

12.2 Introduce the test specimen into the measurement mechanism and initiate the measurement sequence

13 Calculation

13.1 The instrument is assumed to be direct reading with all necessary calculations performed internally and automatically

as follows:

13.1.1 The displacements (distances) between each probe and the nearest surface of the wafer are determined (in pairs) at

intervals along the scan pattern The distance between Probe a

and the nearest surface of the wafer is displacement value a.

The distance between Probe b and the nearest surface of the

wafer is displacement value b The probes are separated by the

distance, D, (see Fig 1) Half the difference of each pair of displacements (0.5[b − a]) yields the position z (along the

measurement axis) of the median surface of the wafer at each point with respect to a plane halfway between the upper and lower probes

13.1.2 Gravitational compensation is applied to the median surface by one of the following methods:

13.1.2.1 Representative Wafer Inversion— A wafer

representative of the lot is measured first in a normal and then

in an inverted position The median surface measurement values are determined at each measurement location in each sample orientation The results are added to obtain 0.5

(z normal + z inverted) This cancels the effect of the representative wafer’s shape while retaining the effect of gravity, resulting in

a value of each measurement point expressed as z gravity The effect of gravity on subsequent measurements on a sample

wafer is cancelled by subtracting z gravity from z normalto produce

z compensatedat each measurement point

N OTE 4—The representative wafer inversion technique deals not only with first-order gravitational effects, but also with other effects that may influence the measured value, such as wafer-periphery effects, some machine-specific signature, etc.

3

13.1.2.2 Sample Wafer Inversion—Each sample wafer is

measured in a normal position then in an inverted position The

median surface measurement values are determined at each

measurement location in each measurement orientation One

half the difference between the normal and inverted

measurement values at each point yields the sample wafer’s

gravity-compensated shape:

z com5z nor 2 z inv

where:

z com 5 compensated position at each measurement point,

z nor 5 normal position at each measurement point, and

z inv 5 inverted position at each measurement point

13.1.2.3 Theoretical Modeling—Measure each sample

wafer and apply gravitational correction that has been

developed from a theoretical model A rigorous model is not

known to exist although approximate corrections have been

calculated.6

13.1.3 A reference plane is constructed that is a

least-squares fit to the median surface z-position data at all points of

the scan pattern The z-value of the reference plane (z ref) is

subtracted from the measured z-position at each point at all the

points of the scan pattern to yield reference plane deviation

(RPD) at each point:

13.2 The difference between the largest (most positive) and

smallest (most negative) of the reference plane deviations is

taken as the warp:

13.3 Record the calculated warp value

13.4 For referee or other measurements where the wafer is

measured more than once, calculate the maximum, minimum, sample standard deviation, average and range of all measurements on the sample

14 Report

14.1 Report the following information:

14.1.1 Date, time and temperature of test, 14.1.2 Identification of operator,

14.1.3 Identification of measuring instruments, including wafer holding device diameter, data point spacing, sensor size, and gravitational correction method,

14.1.4 Lot identification, including nominal diameter and center point thickness,

14.1.5 Description of sampling plan, and 14.1.6 Warp of each wafer measured

14.2 For referee tests the report shall also include the standard deviation of each set of wafer measurements

15 Precision and Bias

15.1 Interlaboratory evaluation of this test method is planned to verify its suitability and reliability Until the results are established, use of this test method for commercial transactions is not recommended unless the parties to the test establish the degree of correlation that can be obtained 15.2 No standards exist against which the bias of this test method can be evaluated

N OTE 5—For further information on producing related reference materials to certify the wafer artifacts contact Subcommittee F1.95.

N OTE 6—Since no standard reference material exists for the measurement of warp, the measurement analysis shall include the capability to calibrate warp results to standards agreed upon between the participants in the measurement.

16 Keywords

16.1 noncontact measurement; semiconductor; shape; silicon; wafers; warp

ANNEX (Mandatory Information) A1 COMPARING DATA SETS A1.1 Introduction

A1.1.1 In qualifying a measurement system for operation, it

can be useful to compare the values ascribed to an artifact such

as a reference standard against those obtained for that artifact

on a machine under test This annex outlines a way in which

the multiple measurement data points that generate a

single-value quantity of warp can be used to monitor the effects of

Interferences more informatively than by using that

single-value alone

A1.1.2 A data set is that set of data used in computation of

warp It is corrected data, that is, all possible after interferences

have been removed and the data replanarized in accordance

with this test method

A1.1.3 A referee wafer (artifact) is accompanied by its own data set (referee data set (RDS)), in which each data point is the average of a number of values obtained for that point over a number of “passes” (repeat measurements) The artifact is measured on a machine under test and its RDS is compared against the resultant measured sample data set Delta-point, delta-warp and other values are computed from the differences The parameter used to determine agreement between the artifact and the system under test and the acceptable level of this agreement is to be agreed upon between the using parties

A1.2 Summary of Test Method

A1.2.1 Select a referee wafer of appropriate criteria, for which an RDS has been obtained

6 Application Note; Gravitational Sag in Silicon Wafers, ADE Corporation, 77

Rowe Street, Newton, MA 02166.

4

A1.2.2 Measure the referee wafer on the machine under test

to obtain a sample data set (SDS)

A1.2.3 Subtract the two to obtain a difference data set

(DDS):

A1.2.4 The DDS represents the differences between the

measurements made on the machine under test and the referee

data set The DDS contains many values The simplest metric

that can be used to determine acceptability is maximum

difference, the largest absolute value in the DDS This

represents the worst-case disagreement between the machine

under test and the referee data

A1.2.5 Accept the machine as suitable for measurement if the maximum difference is less than a value that is agreed upon between the parties to the test

A1.2.6 More complex calculations may also be used, for example, a histogram of the (point-by-point) values of the DDS along with statistical measures (mean, sigma, etc.) may be compared These measures can be compared to application-specific limits or used to provide insight into the nature and source of the difference, or both

APPENDIXES (Nonmandatory Information) X1 VISUALIZATION OF WARP

X1.1 To calculate warp for a given case, it may be

convenient to transform the measurement geometry and to

consider the distance between the upper surface of the wafer

and a reference plane as d1, taken to be positive above the plane

and negative below, and the distance between the lower surface

of the wafer and the reference plane as d2, taken to be positive

below the plane and negative above it, as indicated in the

example in Fig X1.1

RPD5d12 d2

where:

RPD 5 reference plane deviation,

d1 5 distance between upper surface of the wafer, and

d2 5 distance between lower surface of the wafer

X1.2 See Fig X1.2 for examples of warped wafers with

stylized shapes Sample 4 in Fig X1.2 represents the example

Calculations for warp of each of these examples is given in

Table X1.1

FIG X1.1 Visualization of Warp

N OTE 1—T1is two units, T2is four units, and T3is three units; the warp values are calculated from Eq 2 The individual measured distances and the calculated differences are shown in Table X1.1.

FIG X1.2 Visualization of Warp—Stylized Examples

5

X2 MEASUREMENT ERRORS DUE TO DIFFERENCES IN DIAMETER AND THICKNESS BETWEEN A REPRESENTATIVE

WAFER AND A WAFER UNDER TEST

X2.1 For small variations about the calibration values, the

relative change of the gravity effect is four times the relative

change of the diameter and minus two times the relative change

of thickness The following gives examples of gravity effect

errors (in micrometres), that is, deflection at the wafer edge

relative to the wafer center point, using a value of 1.603 10

12for Young’s modulus with the wafer supported horizontally

by a point located at the wafe center point Standard thickness and diameter tolerances in accordance with SEMI Specification

M 1 are used for the calculations, given in Fig X2.1 X2.2 The deflection induced in a wafer by gravity is modeled as follows:

TABLE X1.1 Values for Fig X1.2

6

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This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years and

if not revised, either reapproved or withdrawn Your comments are invited either for revision of this standard or for additional standards and should be addressed to ASTM Headquarters Your comments will receive careful consideration at a meeting of the responsible technical committee, which you may attend If you feel that your comments have not received a fair hearing you should make your views known to the ASTM Committee on Standards, 100 Barr Harbor Drive, West Conshohocken, PA 19428.

Actual Diameter (mm) Typical Deflection (µm) for Nominal Thickness/

* * * * * * *

Actual Diameter (mm)

* * * * * * *

Actual Diameter (mm)

* * * * * * *

Actual Diameter (mm)

* * * * * * *

Actual Diameter (mm)

N OTE 1—the Deflection induced in a wafer by gravity is modeled as follows:

to get relative (9percentage9) errors:

S5kD 4

T2 5 gravity effect ~“sag”!

dS

dD 54

kD3

T2 dS

dD 5 22

kD4

T3 dS

S 54

dD D dS

S 5 22dT T

FIG X2.1 Examples of Gravity Effect Errors

7